A new Newton-Landweber iteration for nonlinear inverse problems

In this paper, we propose a new Newton-Landweber iteration for nonlinear inverse problems. We show the convergence of this method without any convergence rate under a weak nonlinearity condition. Also, this iteration will converge and inherit a certain monotonicity of the iteration error like Landweber iteration, if we restrict our inner iteration steps. Furthermore, we obtain optimal convergence rate of the new Newton-Landweber iteration under stronger nonlinearity conditions and parameter choice rules. Numerical experiments have shown some attractive results.